Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems

TL;DR

This paper investigates deviations from the log-normal distribution in quantum Hall systems at criticality, introducing a new parameter to quantify multifractality beyond the parabolic approximation, supported by analytical and numerical results.

Contribution

It introduces a new parameter to measure deviations from lognormality in multifractal distributions and applies it to quantum Hall systems at criticality.

Findings

Deviations from log-normality are quantified using the new parameter.

Exact calculations for the two-measure random Cantor set demonstrate the approach.

Numerical simulations reveal non-parabolic multifractality in quantum Hall eigenstates.

Abstract

Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two--measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau--band is analyzed.